1093 
tae normal component of the velocity of the fluid has to correspond 
to the normal component of the velocity of the body; the tangential 
velocity is not bound, so that generally the fluid will slip along the 
body. Here a boundary layer exists, and vorticity is formed *). 
I have tried to represent this solution for the case of the two- 
dimensional flow along a cylinder with circular section. The 
radius of the cylinder and the velocity U have both been taken 
= 1. The vortex domain lies therefore between y — + 1 and 
y=—1. Equation (14c) gives then: dv,*/dy = 0; and as on the 
v-axis vy* = (because of the symmetry) we have everywhere 
v,* = 0. On the line y=--1 v changes abruptly by the amount: 
1—v*; between y= -+1 and y= —1 the vorticity is: 
dv* (16 
1) === 6 . . . . . . . . 
dy ) 
In order to find an approximate value for p‚ | have put: 
N A, cosn@ 
a Ag lta ee Pe. eo GET) 
1 ny 
(6 =O is the point most in front of the circle, where «= +1; 
at the opposite point 6 =a). Then the boundary conditions (146) 
and (14c) become: 
N 
SOS: ao Acos mn Of CORONES) 
0 
N 
ae E (n+1) Aycos(n+1)O=0 . (182) 
0 
By means of the method of least squares a solution has been 
sought that for a given value of N satisfies as well as possible 
(18a) and (186). For N==8 is found in this way: 
A, = + 0,374 
A, = + 0,375 
A, == + 0,248 
A, = + 0,086 
With the aid of these numbers fig. 13 has been drawn for the 
absolute flow and fig. 14 for the relative flow. 
) Lc. p. 252; further also p. 623 and 1144. 
OsSEEN considers moreover the following simple cases (lc. p. 249/250): 
a. Body illimited in ‘backward direction (the thickness has no maximum at a 
finite distance). Everywhere outside the body we have irrotational motion, defined by 
(13a), (14a) and (145). 
b. Body illimited in front direction. Then a solution of (144) and (14c) is given 
by: p=0 (we have no front, so that (14b) vanishes). Outside the cylinder 
v = 0; inside vy = U. 
